Individual penalty based constraint handling using a hybrid bi-objective and penalty function approach

Abstract

The holy grail of constrained optimization is the development of an efficient, scale invariant and generic constraint handling procedure in single and multi-objective constrained optimization problems. In this paper, an individual penalty parameter based methodology is proposed to solve constrained optimization problems. The individual penalty parameter approach is a hybridization between an evolutionary method, which is responsible for estimation of penalty parameters for each constraint and the initial solution for local search. However the classical penalty function approach is used for its convergence property. The aforesaid method adaptively estimates penalty parameters linked with each constraint and it can handle any number of constraints. The method is tested over multiple runs on six mathematical test problems and a engineering design problem to verify its efficacy. The function evaluations and obtained solutions of the proposed approach is compared with three of our previous results. In addition to that, the results are also verified with some standard methods taken from literature. The results show that our method is very efficient compared to some recently developed methods.